Obviously the foundational problem with trying to address things effecting the whole world is having a valid determination of what is needing to be done given the size of the problem itself.  If you must have a body of governance, I would suggest that it be required to have as much openness and diversity in it administrating, and with as much freedom for all, as possible.  South Africa's constitution comes to mind as an expression of governance that points strongly in that direction.  

 Presuming that man, as a whole has determined properly.  Then the matter becomes, how to best resolve that into a behavior that is not abusable; either by manipulators in the governing process, or by processes that are impossible to really oversee or verify.  Otherwise, that may the main product generated, instead of the desired goal.  Ideally it is best to just get the masses as fully informed as possible.  Then the vast multitudes are working on solutions that governing systems may never have the time or resources to soberly endeavor.

  Lets note the climate change concern.  It is said that China is one of the major contributors as a carbon dioxide generator.  Yet it seems to me that any solution that is presently being considered puts them in even a better financial position.  Perhaps if the nations of the world had a charity tariff on the items they made in factories that produced what their own country considered excessive carbon emissions, and put those funds only into making systems that were more in line with what their own country allows; then that might make something change.  At the very least it would allow those countries economies to compete against high carbon emitters, and so stay financially viable in their endeavor of seeking better ways to address climate concerns, and the likes.

  On this next matter I have little in a way to verify anything.   Yet I wonder if there has been emissions purposely generated that are contrary to the green house effect.  One scientist reported on PBS recently that putting a garden hose flow of a sulfur compound very high into the air at the polar regions would be a viable temporary fix to the present climate concern.  The poles are critical, since they harbor large reservoirs of methane in the permafrost ice.  The sulfur idea is only a temporary fix, though.  From what I've heard, if enough carbon dioxide get in the oceans it leads to the lost of its ability to absorb carbon dioxide by making limestone through the diatoms and shellfish it harbors.  [The forum has a bit more detail on it, and will let you respond  (just register, or sign in).   Look under "All Comments" for topics.  Add one if you wish...]

  So I'd say the greatest present need at the world level as it relates to climate change is a verifiable monitoring process, as there are quite a number of factors involved; most of which require monitoring vast areas of the planet.  Recently, some signs suggest that the rate of warming is not going up in some places.  So verifiable details to be able to make sound determinations is needed most of all ...  Yes the world needs order, but an order mainly by enlightening minds, and not generating conditions that may be more dominating, or oppressive, than what is notably likely to occur. 

  In general the worlds people need a basic amount of resources for each [healthily related to realities limitations] to be cultivated while also having national borders being respected.  This regionalism not only respects the present order of governance.  It ideally should help focus its potentials in viably manageable 'units' for generating abundance, that ultimately can also be the needed help for others.  And perhaps competitive 'institutions' that cultivate people to their fullest, so they can make wise decisions, and function and relate, as best as humans can with all the potentials that are allowed by that God given nature, is the best way to deal with the errancies larger systems, of governance (or otherwise) happen to crop up.  That I can buy as being a functional process.